Make a plot (sketch) of a “triangle wave”, i.e. a function that is periodic in time with period \(T\), that increrases linearly from a value \(-A\) to a value \(A\) in time \(T/2\), then decreases linearly to \(-A\) in time \(T/2\), and is repeated endlessly. Write down the equation that describes this waveform in one period (it is a piecewise function).
Calculate the Fourier coefficients for this triangle wave. It is most convenient to choose the time origin to make the function either even or odd (why?). Whatever time origin you choose, say whether that choice makes the function odd, even, or neither.
Make a plot (now use a program like Mathematica) of the triangle waveform and on the same plot, th approximation using the first few terms (2 or 3) and also the approximation using a larger number (10 or more). This gives a visual evaluation of how well the series converges.